PRP Records

Probable Primes Top 10000

(277054 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
600121690^17959+17959^2169092276Hans Havermann08/2020
6002(7613^23773-1)/761292273Serge Batalov08/2020
6003(31*2^306487-1)/229192260Lelio R Paula02/2014
60042^306467-183561192256Enzo Doria04/2015
60052^306433+7642792246Enzo Doria05/2016
60072^306430-11331392245Enzo Doria07/2014
6006(23*10^92244-59)/992245Robert Price03/2017
6008(47*2^306398+1)/138480392231Lelio R Paula04/2015
600921436^20043+20043^2143692217Hans Havermann09/2020
6010(25*10^92186+59)/392187Robert Price05/2016
60112^306213-28618392180Enzo Doria06/2015
601210^92178+6192179Robert Price04/2011
601310^92178-17550992178Patrick De Geest07/2013
60142^306200+118592176Lelio R Paula02/2016
6015(2^306171+1514)/292167Stefano Morozzi09/2020
60162^306153+1192162Lelio R Paula11/2012
6017(2^306141-7)/592157Lelio R Paula06/2013
601821725^17454+17454^2172592156Hans Havermann09/2020
6019(26*10^92152-23)/392153Robert Price08/2016
6020(2*10^92152+67)/392152Robert Price04/2017
602121368^20457+20457^2136892115Hans Havermann08/2020
6022(2^305996+3018)/292114Stefano Morozzi09/2020
60234*10^92099+3*7^9209992100Mike Oakes12/2010
602430504^1045+1045^3050492096Hans Havermann08/2020
602524334^6085+6085^2433492087Hans Havermann08/2020
6026(2^305898+2262)/292085Stefano Morozzi01/2021
6027(4591^25147-1)/459092083Serge Batalov08/2020
6028115^44684+11492081Norbert Schneider07/2018
6029(416771^16384+1)/292077Richard Fischer08/2020
6030(2^305867-2^152934+1)/59207511/2006
60312^305851-10949592071Enzo Doria04/2014
6032(416213^16384+1)/292067Richard Fischer08/2020
603412^85300+3592055Lelio R Paula06/2016
6033((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
603521732^17201+17201^2173292048Hans Havermann08/2020
60367*10^92043-3992044Robert Price07/2020
60373^192911+9292042Lelio R Paula04/2016
60382^305723-27627192032Enzo Doria07/2015
6039(2^305714+3738)/292029Stefano Morozzi09/2020
6040(2^305707+798)/292027Stefano Morozzi01/2021
6041(2^305682+3202)/292020Stefano Morozzi09/2020
60422^305676+9392018Donovan Johnson06/2008
60433^192819+491999Lelio R Paula04/2013
6044(38*10^91997-83)/9991997Ray Chandler07/2011
60452^305539+7291191977Enzo Doria04/2016
6046Phi(212014,10)91960Makoto Kamada04/2019
6047(2^305423+2666)/291942Stefano Morozzi09/2020
6048(2^305427-5)/129799821391934Lelio R Paula06/2013
604982077!4-12891928Robert Price11/2019
605085^47642+8491922Norbert Schneider10/2015
605110^91920+18765191921Patrick De Geest07/2013
605210^91920-3991920Robert Price05/2011
6053(3975^25537-1)/397491913Serge Batalov08/2020
6054(22*10^91903+41)/991904Robert Price02/2015
60562^305275-2791897Lelio R Paula11/2012
60553^192607-772691897Enzo Doria05/2014
6057(2^305220+1278)/291881Stefano Morozzi01/2021
6058(6958^23911-1)/695791874Serge Batalov08/2020
6059(7*10^91856-61)/991856Erik Branger12/2009
6060(2^305107+1274)/291847Stefano Morozzi01/2021
6061(89*10^91839-53)/991840Robert Price11/2015
60621678^28479+28479^167891839Norbert Schneider08/2020
60638*5^131351+791812Lelio R Paula10/2014
60643^192426-6891811Lelio R Paula04/2016
60662^304973+11791807Lelio R Paula11/2012
6065(2^304974+234)/291807Stefano Morozzi09/2020
60672^304939-186372791796Enzo Doria03/2016
60682^304902+841591785Lelio R Paula02/2016
606918^73119+6191785Lelio R Paula06/2016
6070(78557*2^304740+1)/15991739Lelio R Paula06/2014
60712^304747+7135591738Lelio R Paula02/2016
6072(2^304738+2262)/291735Stefano Morozzi01/2021
60738*3^192251+591728Lelio R Paula08/2014
6074(2^304693+3746)/291722Stefano Morozzi01/2021
60752^304674-8791717Lelio R Paula11/2012
6076(28*10^91715+701)/991716Robert Price11/2017
6078(2^304698+9)/136280995391715Lelio R Paula06/2013
6077(2^304671+1046)/291715Stefano Morozzi09/2020
6079(2^304667+3614)/291714Stefano Morozzi09/2020
6080(5*10^91707-119)/391708Robert Price04/2016
60812^304633-11277191704Enzo Doria06/2014
6082(395347^16384+1)/291701Richard Fischer06/2020
60839*10^91693+2391694Robert Price11/2017
60842^304578-1671391688Enzo Doria05/2013
60856^117824-1871391685Enzo Doria03/2013
6086(17^74509-1)/1691679Paul Bourdelais03/2010
6087(2^304551-7)/891223191673Lelio R Paula06/2013
6088(2^304532-3)/301391670Lelio R Paula06/2013
60892^304507-1664591666Enzo Doria04/2013
6090(29*2^304489+1)/3191661Lelio R Paula09/2013
609121221^20860+20860^2122191661Hans Havermann08/2020
60922^304471-183612791655Enzo Doria04/2015
60932^304433+3276991644Lelio R Paula02/2016
60942^304410-1662591637Enzo Doria04/2013
6095183^40500-291630Lelio R Paula10/2017
6096(203*10^91613+1)/391615Robert Price09/2017
60974*5^131052+791603Lelio R Paula10/2014
609821725^16458+16458^2172591601Hans Havermann08/2020
60992^304278-400191597Yves Minet04/2017
61002^304272-186637791595Enzo Doria03/2016
61012^304268+1968391594Lelio R Paula02/2016
610221718^16497+16497^2171891594Hans Havermann08/2020
610322759^10576+10576^2275991590Hans Havermann08/2020
61042^304162-16191562Lelio R Paula11/2012
61055*7^108331+691552Lelio R Paula10/2014
61062^304082-278782191538Enzo Doria03/2016
61072^304015+6413391518David Broadhurst06/2002
6108(7*2^303963+1)/391503Lelio R Paula09/2013
6109(2^303945-9)/361791494Lelio R Paula06/2013
6110(384007^16384+1)/291494Richard Fischer05/2020
61112^303930+188052791493Enzo Doria10/2016
611224810^4859+4859^2481091464Hans Havermann08/2020
61133^191684-6891457Lelio R Paula04/2016
6114(21*2^303813-1)/16991456Lelio R Paula02/2014
6115(298*10^91446+11)/391448Robert Price11/2020
611611^87797-12091432Enzo Doria07/2012
61172^303698-184723191423Enzo Doria07/2015
6118(38^28933-1)^2-291416Norbert Schneider06/2016
611925660^3643+3643^2566091388Hans Havermann08/2020
61202^303554+7729991379Enzo Doria05/2016
61212^303542+1270591376Lelio R Paula02/2016
612231^61269-291375Lelio R Paula09/2013
6123(2^303525+2774)/291370Stefano Morozzi01/2021
61242^303516-6487591368Lelio R Paula02/2016
6125(2^303497+1266)/291362Stefano Morozzi09/2020
6126(2^303497+3710)/291362Stefano Morozzi09/2020
612721856^15121+15121^2185691349Hans Havermann09/2020
6128(24737*2^303428+1)/391345Lelio R Paula06/2014
6129(21181*2^303357+1)/3236191320Lelio R Paula06/2014
613023081^9046+9046^2308191319Hans Havermann09/2020
61312^303344-278696991316Enzo Doria03/2016
61326^117346+6591313Lelio R Paula05/2016
61332^303321+85591309Lelio R Paula02/2016
6134(2^303315+3746)/291307Stefano Morozzi01/2021
613512^84606+4791306Lelio R Paula06/2016
61362^303288+187431191299Enzo Doria06/2016
6137197^39788-291293Lelio R Paula10/2017
613811^87663-171091292Enzo Doria12/2012
61392^303224+253391280Henri Lifchitz05/2005
61406^117302+14391279Lelio R Paula05/2016
61413^191306-11288091277Enzo Doria07/2014
6142(10052^22807-1)/1005191276Serge Batalov08/2020
61432^303207+1291591275Lelio R Paula02/2016
61442^303191-11125991270Enzo Doria05/2014
614581539!4+3291267Robert Price09/2019
6146(2^303116+3570)/291247Stefano Morozzi09/2020
614710^91230+9^(91230+1)91231Robert Price08/2016
614810^91230+792191231Patrick De Geest11/2016
614910^91230-91114191230Patrick De Geest11/2016
615010^91229+34879391230Patrick De Geest07/2019
615110^91229-247191229Patrick De Geest01/2019
61522996^26241+26241^299691228Norbert Schneider01/2020
615410^91225+527191226Patrick De Geest01/2019
61532816^26445+26445^281691226Norbert Schneider02/2020
61566^117232-1742391225Enzo Doria02/2013
615510^91225-14721991225Patrick De Geest07/2019
61577*10^91215+391216Erik Branger11/2009
615810^91215+23061191216Patrick De Geest07/2019
615910^91215-453991215Patrick De Geest01/2019
6160(2^303007+606)/291214Stefano Morozzi09/2020
6161(2^302998+3102)/291212Stefano Morozzi09/2020
616210^91210+242191211Patrick De Geest01/2019
616310^91210-173791210Patrick De Geest01/2019
616497*10^91205-391207Robert Price01/2017
61652^302979-16118191206Enzo Doria04/2013
6166(166*10^91199-7)/391201Robert Price11/2020
61672^302949+8191197Henri Lifchitz02/2007
616810^91194+20036191195Patrick De Geest07/2019
61704*6^117192-591194Lelio R Paula10/2014
616910^91194-866391194Patrick De Geest01/2019
61712^302918+9991188Lelio R Paula11/2012
617210^91186+26811191187Patrick De Geest07/2019
617310^91186-776391186Patrick De Geest01/2019
617410^91181+55047191182Patrick De Geest07/2019
617510^91181-136791181Patrick De Geest01/2019
617610^91178+7188391179Patrick De Geest07/2019
617710^91178-471991178Patrick De Geest01/2019
617824686^4935+4935^2468691173Hans Havermann08/2020
617910^91165+304391166Patrick De Geest01/2019
618010^91165-39941391165Patrick De Geest07/2019
618110^91156+386191157Patrick De Geest01/2019
618210^91156-23149791156Patrick De Geest07/2019
61832^302797+186958791151Enzo Doria05/2016
6184265^37614+37614^26591148Norbert Schneider01/2015
61857^107852+8291146Lelio R Paula04/2016
6186(38*10^91144-11)/991145Robert Price05/2015
6187(55*10^91142+377)/991143Robert Price10/2017
618810^91128+996191129Patrick De Geest01/2019
6190249^38030+38030^24991128Norbert Schneider01/2015
618910^91128-18915391128Patrick De Geest07/2019
61916^117094-21104991117Mike Oakes05/2011
619221353^18472+18472^2135391103Hans Havermann05/2020
61932^302602-186718191093Enzo Doria03/2016
619410^91092+5612791093Patrick De Geest07/2019
619510^91092-910791092Patrick De Geest01/2019
6196(1017*2^302592-1)/5391091Lelio R Paula04/2015
619715^77445-1691083Lelio R Paula07/2016
619821656^16053+16053^2165691076Hans Havermann05/2020
61992^302505+8191064Henri Lifchitz02/2007
62002^302496-11234991061Enzo Doria06/2014
6201(2^302475+1790)/291054Stefano Morozzi01/2021
620217^73999-7291052Lelio R Paula07/2016
620310^91047+933191048Patrick De Geest01/2019
620410^91047-67116991047Patrick De Geest07/2019
620510^91044+207791045Patrick De Geest01/2019
620610^91044-13635991044Patrick De Geest07/2019
620710^91041+934991042Patrick De Geest01/2019
620810^91041-782391041Patrick De Geest01/2019
620910^91040+407791041Patrick De Geest01/2019
621010^91040-11942191040Patrick De Geest07/2019
621110^91037+276991038Patrick De Geest01/2019
621210^91037-2264991037Patrick De Geest07/2019
6213(16*10^91032+41)/391033Robert Price10/2017
621410^91023+5803991024Patrick De Geest07/2019
621510^91023-647191023Patrick De Geest01/2019
621610^91018+787391019Patrick De Geest01/2019
621710^91018-33317791018Patrick De Geest07/2019
621810^91017+6876791018Patrick De Geest07/2019
621910^91017-42832791017Patrick De Geest07/2019
622010^91016+7311191017Patrick De Geest07/2019
622110^91016-797391016Patrick De Geest01/2019
62221949^27666+27666^194991016Norbert Schneider04/2020
62232^302332+57729457591012Lelio R Paula08/2016
622410^91004+907391005Patrick De Geest01/2019
622510^91004-49151991004Patrick De Geest07/2019
622610^91003+7426991004Patrick De Geest07/2019
622710^91003-390391003Patrick De Geest01/2019
62282^302274+7420990994Enzo Doria04/2016
622910^90991+8114790992Patrick De Geest07/2019
623010^90991-627990991Patrick De Geest01/2019
623110^90983+139390984Patrick De Geest01/2019
623211*10^90982+990984Robert Price08/2020
623310^90983-56238390983Patrick De Geest07/2019
6234(311^36497-1)/31090976Eric Chen09/2017
6235(2^302210+1014)/290974Stefano Morozzi09/2020
6236(3^190668+2)/8990970Lelio R Paula04/2013
62372^302188+9019590968Lelio R Paula02/2016
6238(53*10^90965-71)/990966Robert Price09/2015
623910^90965+57398790966Patrick De Geest07/2019
624010^90965-683390965Patrick De Geest01/2019
624110^90964+4878990965Patrick De Geest07/2019
624210^90964-5210390964Patrick De Geest07/2019
624310^90963+19188990964Patrick De Geest07/2019
624410^90963-365990963Patrick De Geest01/2019
624510^90962+765790963Patrick De Geest01/2019
624610^90962-21563390962Patrick De Geest07/2019
624710^90961+6747190962Patrick De Geest07/2019
624810^90961-21104390961Patrick De Geest07/2019
624910^90960+107211790961Patrick De Geest07/2019
625010^90959+879190960Patrick De Geest01/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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